arm_convolution_example_f32.c
1 /* ---------------------------------------------------------------------- 2 * Copyright (C) 2010-2012 ARM Limited. All rights reserved. 3 * 4 * $Date: 17. January 2013 5 * $Revision: V1.4.0 6 * 7 * Project: CMSIS DSP Library 8 * Title: arm_convolution_example_f32.c 9 * 10 * Description: Example code demonstrating Convolution of two input signals using fft. 11 * 12 * Target Processor: Cortex-M4/Cortex-M3 13 * 14 * Redistribution and use in source and binary forms, with or without 15 * modification, are permitted provided that the following conditions 16 * are met: 17 * - Redistributions of source code must retain the above copyright 18 * notice, this list of conditions and the following disclaimer. 19 * - Redistributions in binary form must reproduce the above copyright 20 * notice, this list of conditions and the following disclaimer in 21 * the documentation and/or other materials provided with the 22 * distribution. 23 * - Neither the name of ARM LIMITED nor the names of its contributors 24 * may be used to endorse or promote products derived from this 25 * software without specific prior written permission. 26 * 27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 31 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 32 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 33 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 34 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN 37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 38 * POSSIBILITY OF SUCH DAMAGE. 39 * -------------------------------------------------------------------- */ 40 41 /** 42 * @ingroup groupExamples 43 */ 44 45 /** 46 * @defgroup ConvolutionExample Convolution Example 47 * 48 * \par Description: 49 * \par 50 * Demonstrates the convolution theorem with the use of the Complex FFT, Complex-by-Complex 51 * Multiplication, and Support Functions. 52 * 53 * \par Algorithm: 54 * \par 55 * The convolution theorem states that convolution in the time domain corresponds to 56 * multiplication in the frequency domain. Therefore, the Fourier transform of the convoution of 57 * two signals is equal to the product of their individual Fourier transforms. 58 * The Fourier transform of a signal can be evaluated efficiently using the Fast Fourier Transform (FFT). 59 * \par 60 * Two input signals, <code>a[n]</code> and <code>b[n]</code>, with lengths \c n1 and \c n2 respectively, 61 * are zero padded so that their lengths become \c N, which is greater than or equal to <code>(n1+n2-1)</code> 62 * and is a power of 4 as FFT implementation is radix-4. 63 * The convolution of <code>a[n]</code> and <code>b[n]</code> is obtained by taking the FFT of the input 64 * signals, multiplying the Fourier transforms of the two signals, and taking the inverse FFT of 65 * the multiplied result. 66 * \par 67 * This is denoted by the following equations: 68 * <pre> A[k] = FFT(a[n],N) 69 * B[k] = FFT(b[n],N) 70 * conv(a[n], b[n]) = IFFT(A[k] * B[k], N)</pre> 71 * where <code>A[k]</code> and <code>B[k]</code> are the N-point FFTs of the signals <code>a[n]</code> 72 * and <code>b[n]</code> respectively. 73 * The length of the convolved signal is <code>(n1+n2-1)</code>. 74 * 75 * \par Block Diagram: 76 * \par 77 * \image html Convolution.gif 78 * 79 * \par Variables Description: 80 * \par 81 * \li \c testInputA_f32 points to the first input sequence 82 * \li \c srcALen length of the first input sequence 83 * \li \c testInputB_f32 points to the second input sequence 84 * \li \c srcBLen length of the second input sequence 85 * \li \c outLen length of convolution output sequence, <code>(srcALen + srcBLen - 1)</code> 86 * \li \c AxB points to the output array where the product of individual FFTs of inputs is stored. 87 * 88 * \par CMSIS DSP Software Library Functions Used: 89 * \par 90 * - arm_fill_f32() 91 * - arm_copy_f32() 92 * - arm_cfft_radix4_init_f32() 93 * - arm_cfft_radix4_f32() 94 * - arm_cmplx_mult_cmplx_f32() 95 * 96 * <b> Refer </b> 97 * \link arm_convolution_example_f32.c \endlink 98 * 99 */ 100 101 102 /** \example arm_convolution_example_f32.c 103 */ 104 105 #include "arm_math.h" 106 #include "math_helper.h" 107 108 #if defined(SEMIHOSTING) 109 #include <stdio.h> 110 #endif 111 112 /* ---------------------------------------------------------------------- 113 * Defines each of the tests performed 114 * ------------------------------------------------------------------- */ 115 #define MAX_BLOCKSIZE 128 116 #define DELTA (0.000001f) 117 #define SNR_THRESHOLD 90 118 119 /* ---------------------------------------------------------------------- 120 * Declare I/O buffers 121 * ------------------------------------------------------------------- */ 122 float32_t Ak[MAX_BLOCKSIZE]; /* Input A */ 123 float32_t Bk[MAX_BLOCKSIZE]; /* Input B */ 124 float32_t AxB[MAX_BLOCKSIZE * 2]; /* Output */ 125 126 /* ---------------------------------------------------------------------- 127 * Test input data for Floating point Convolution example for 32-blockSize 128 * Generated by the MATLAB randn() function 129 * ------------------------------------------------------------------- */ 130 float32_t testInputA_f32[64] = 131 { 132 -0.808920, 1.357369, 1.180861, -0.504544, 1.762637, -0.703285, 133 1.696966, 0.620571, -0.151093, -0.100235, -0.872382, -0.403579, 134 -0.860749, -0.382648, -1.052338, 0.128113, -0.646269, 1.093377, 135 -2.209198, 0.471706, 0.408901, 1.266242, 0.598252, 1.176827, 136 -0.203421, 0.213596, -0.851964, -0.466958, 0.021841, -0.698938, 137 -0.604107, 0.461778, -0.318219, 0.942520, 0.577585, 0.417619, 138 0.614665, 0.563679, -1.295073, -0.764437, 0.952194, -0.859222, 139 -0.618554, -2.268542, -1.210592, 1.655853, -2.627219, -0.994249, 140 -1.374704, 0.343799, 0.025619, 1.227481, -0.708031, 0.069355, 141 -1.845228, -1.570886, 1.010668, -1.802084, 1.630088, 1.286090, 142 -0.161050, -0.940794, 0.367961, 0.291907 143 144 }; 145 146 float32_t testInputB_f32[64] = 147 { 148 0.933724, 0.046881, 1.316470, 0.438345, 0.332682, 2.094885, 149 0.512081, 0.035546, 0.050894, -2.320371, 0.168711, -1.830493, 150 -0.444834, -1.003242, -0.531494, -1.365600, -0.155420, -0.757692, 151 -0.431880, -0.380021, 0.096243, -0.695835, 0.558850, -1.648962, 152 0.020369, -0.363630, 0.887146, 0.845503, -0.252864, -0.330397, 153 1.269131, -1.109295, -1.027876, 0.135940, 0.116721, -0.293399, 154 -1.349799, 0.166078, -0.802201, 0.369367, -0.964568, -2.266011, 155 0.465178, 0.651222, -0.325426, 0.320245, -0.784178, -0.579456, 156 0.093374, 0.604778, -0.048225, 0.376297, -0.394412, 0.578182, 157 -1.218141, -1.387326, 0.692462, -0.631297, 0.153137, -0.638952, 158 0.635474, -0.970468, 1.334057, -0.111370 159 }; 160 161 const float testRefOutput_f32[127] = 162 { 163 -0.818943, 1.229484, -0.533664, 1.016604, 0.341875, -1.963656, 164 5.171476, 3.478033, 7.616361, 6.648384, 0.479069, 1.792012, 165 -1.295591, -7.447818, 0.315830, -10.657445, -2.483469, -6.524236, 166 -7.380591, -3.739005, -8.388957, 0.184147, -1.554888, 3.786508, 167 -1.684421, 5.400610, -1.578126, 7.403361, 8.315999, 2.080267, 168 11.077776, 2.749673, 7.138962, 2.748762, 0.660363, 0.981552, 169 1.442275, 0.552721, -2.576892, 4.703989, 0.989156, 8.759344, 170 -0.564825, -3.994680, 0.954710, -5.014144, 6.592329, 1.599488, 171 -13.979146, -0.391891, -4.453369, -2.311242, -2.948764, 1.761415, 172 -0.138322, 10.433007, -2.309103, 4.297153, 8.535523, 3.209462, 173 8.695819, 5.569919, 2.514304, 5.582029, 2.060199, 0.642280, 174 7.024616, 1.686615, -6.481756, 1.343084, -3.526451, 1.099073, 175 -2.965764, -0.173723, -4.111484, 6.528384, -6.965658, 1.726291, 176 1.535172, 11.023435, 2.338401, -4.690188, 1.298210, 3.943885, 177 8.407885, 5.168365, 0.684131, 1.559181, 1.859998, 2.852417, 178 8.574070, -6.369078, 6.023458, 11.837963, -6.027632, 4.469678, 179 -6.799093, -2.674048, 6.250367, -6.809971, -3.459360, 9.112410, 180 -2.711621, -1.336678, 1.564249, -1.564297, -1.296760, 8.904013, 181 -3.230109, 6.878013, -7.819823, 3.369909, -1.657410, -2.007358, 182 -4.112825, 1.370685, -3.420525, -6.276605, 3.244873, -3.352638, 183 1.545372, 0.902211, 0.197489, -1.408732, 0.523390, 0.348440, 0 184 }; 185 186 187 /* ---------------------------------------------------------------------- 188 * Declare Global variables 189 * ------------------------------------------------------------------- */ 190 uint32_t srcALen = 64; /* Length of Input A */ 191 uint32_t srcBLen = 64; /* Length of Input B */ 192 uint32_t outLen; /* Length of convolution output */ 193 float32_t snr; /* output SNR */ 194 195 int32_t main(void) 196 { 197 arm_status status; /* Status of the example */ 198 arm_cfft_radix4_instance_f32 cfft_instance; /* CFFT Structure instance */ 199 200 #if defined(SEMIHOSTING) 201 printf("START\n"); 202 #endif 203 204 /* CFFT Structure instance pointer */ 205 arm_cfft_radix4_instance_f32 *cfft_instance_ptr = 206 (arm_cfft_radix4_instance_f32*) &cfft_instance; 207 208 /* output length of convolution */ 209 outLen = srcALen + srcBLen - 1; 210 211 /* Initialise the fft input buffers with all zeros */ 212 arm_fill_f32(0.0, Ak, MAX_BLOCKSIZE); 213 arm_fill_f32(0.0, Bk, MAX_BLOCKSIZE); 214 215 /* Copy the input values to the fft input buffers */ 216 arm_copy_f32(testInputA_f32, Ak, MAX_BLOCKSIZE/2); 217 arm_copy_f32(testInputB_f32, Bk, MAX_BLOCKSIZE/2); 218 219 /* Initialize the CFFT function to compute 64 point fft */ 220 status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 0, 1); 221 222 /* Transform input a[n] from time domain to frequency domain A[k] */ 223 arm_cfft_radix4_f32(cfft_instance_ptr, Ak); 224 /* Transform input b[n] from time domain to frequency domain B[k] */ 225 arm_cfft_radix4_f32(cfft_instance_ptr, Bk); 226 227 /* Complex Multiplication of the two input buffers in frequency domain */ 228 arm_cmplx_mult_cmplx_f32(Ak, Bk, AxB, MAX_BLOCKSIZE/2); 229 230 /* Initialize the CIFFT function to compute 64 point ifft */ 231 status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 1, 1); 232 233 /* Transform the multiplication output from frequency domain to time domain, 234 that gives the convolved output. */ 235 arm_cfft_radix4_f32(cfft_instance_ptr, AxB); 236 237 /* SNR Calculation */ 238 snr = arm_snr_f32((float32_t *)testRefOutput_f32, AxB, srcALen + srcBLen - 1); 239 240 /* Compare the SNR with threshold to test whether the 241 computed output is matched with the reference output values. */ 242 status = (snr <= SNR_THRESHOLD) ? ARM_MATH_TEST_FAILURE : ARM_MATH_SUCCESS; 243 244 if (status != ARM_MATH_SUCCESS) 245 { 246 #if defined (SEMIHOSTING) 247 printf("FAILURE\n"); 248 #else 249 while (1); /* main function does not return */ 250 #endif 251 } 252 else 253 { 254 #if defined (SEMIHOSTING) 255 printf("SUCCESS\n"); 256 #else 257 while (1); /* main function does not return */ 258 #endif 259 } 260 261 } 262 263 /** \endlink */